Seshadri constants and periods of polarized abelian varieties

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The purpose of this paper is to study the Seshadri constants of abelian varieties. Consider a polarized abelian variety (A,L) of dimension g over the field of complex numbers. One can associate to (A,L) a real number e(A,L), its Seshadri constant, which in effect measures how much of the positivity of L can be concentrated at any given point of A. The number e(A,L) can be defined as the rate of growth in k of the number of jets that one can specify in the linear series |OA(kL)|. Alternatively, one considers the blow-up f : X = Blx(X) −→ X of X at a point x with exceptional divisor E ⊂ X over x, and defines e(A,L) =def sup{ e ∈ R | f ∗L− eE is nef } .